Hyperbolic Discounting &

Defense Acquisitions

Eric M. LofgrenTechnomics, Inc.

ICEAA 2015, San Diego11 June 2015 2:30pm; Marina 2

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What is Hyperbolic Discounting?

• Exponential function is smooth with a constant unit discount rate regardless of timeframeo Mirrors expected growth of pecuniary investment opportunities

• Hyperbolic function is steep in the short-term and relatively flat thereaftero Reflects personal valuationso Continually reconsidered at each instance in time

Time Now #1 Time Now #21 2 3 4 5 7 8 9 10

Hyperbolic Discounting

Exponential Discounting

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Impacts of Incomplete Contracting

Source: Air Force Cost Analysis Agency (AFCAA) Contracts Database (Publically Available). Includes 4,073 fixed-price contracts from across the military services dating back to Aug. 1991. Accessed November 11, 2014.

• Extensive requirements documentation cannot offset the need for contract modso Coase: contracting less desirable the longer the term or less specifiable the requirementso Jensen and Meckling: “collocation” of production knowledge and decision-rightso Hayek: gov’t retention of decision-rights necessitates planning on a similar scale as the

contractor themselves and shrouds responsibility for poor performance

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Additional Avenue for Contract Mods

• Significant budget growth due to marginal new scope added to the existing contract vehicleso Consequence of “price aggressively, budget conservatively”

Source: Earned Value Management Central Repository (EVM-CR). Sample includes 11 MDAP Contract Performance Reports (CPRs). BAC stands for Budget at Complete. See http://dau.mil for additional information.

"Fully Informed" Cost Estimate

Contract Bid function if mods

are expected

Winning Bid $?

?subsequent modifications

• The government awards contracts using a procurement, or reverse, auction whereby the lowest bidder wins the worko Each contractor, with equal efficiency assumed for analytical traction, has a “signal” to the

potential contract costso Signal errors are also assumed to be approximately NIID~[0,σ2] “Winner’s Curse”: the winning bid is biased downward and the contractor is expected to make a

loss

• What if contractors anticipate contract modifications which partially alleviates the expected loss of an underestimate?o Market Feedback Problem: firm’s speculation is not disciplined by endogenous profit/loss

feedbacko Too Big to Fail Problem: firm may believe the project or company itself will be bailed out of poor

performance – see also hiding hand principleo How might this effect the winner’s curse problem? (Winner’s Blessing)

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Are Contract Bids Biased Downwards?

"Fully Informed" Cost Estimate

Contract Bid Probability

Density Function

Winning Bid $

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Aggregate Financial Effect of Mods

Source: Google finance accessed through ‘R’ quantmod package. 20 healthcare companies from the NYQ list under Yahoo Biotechnology, Drug Manufactures – Major, and Hospitals. 29 retail companies in NYQ list under Yahoo category names Restaurants, Grocery Stores, and Department Stores. Defense firms include Lockheed Martin, General Dynamics, Boeing, Northrop Grumman, and Raytheon. Second tier defense firms not used because they tend to receive a majority of their revenue from defense primes as opposed to the government itself. Control group of 77 companies from a simple random sample of other company names. Gross Profits as percent of Total Revenues over four years (2010-2013) used to determine mean and standard deviation for each sector, the latter being divided by the former to derive the metric used in the chart.

• DellaVigna and Malmendier (2004): profit-maximizing firms price investment goods below marginal cost for consumers who are overconfident about future self-controlo Back-load fees and transaction costs (e.g. credit cards, health clubs, life insurance, etc.)

• Overpriced new scope translates to high profitability on that work – or the ability to cover overruns on baseline scopeo Defense contractors also may expect to recoup costs through follow-on work

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Linear FPIF Schemes

• When system attributes are proven and stable, performance parameters do not need to be incentivized so much as overall cost reductions through efficiency gainso e.g. 25:75 share ratio means that for every dollar the contractor completes the order less

than the target cost and within the range of incentive effectiveness, 25 cents is returned to the government and the contractor receives 75 cents in addition to the target profit

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Evidence of CAM Time-Inconsistency

• The Baseline Execution Index (BEI) indicates the efficiency with which tasks have been accomplished when measured against the baselineo Despite actual performance (blue) staying flat or falling, the forecast task performance (red)

climbs to implausibly high levelso CAMs within the sample overestimate their ability to execute in the future

Source: Lofgren, Eric. “Trust, but Verify – An Improved Estimating Technique Using the Integrated Master Schedule.” ICEAA 2014.

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Evidence Continued…

• The result of CAMs optimism is that the IMS does not alert management to likely schedule slips until relatively lateo Exhibits the constant repudiation of past planso We would expect forecast performance to reflect actual performance and schedule slips

to be reported earlier if CAMs acknowledged their tendency to discount hyperbolically

Source: Lofgren, Eric. “Trust, but Verify – An Improved Estimating Technique Using the Integrated Master Schedule.” ICEAA 2014.

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Incentivized Commitment Scheme

• For production with long time horizons, lags between work output and subsequent revenues generate suboptimal effort in the early stageso Kaur, Kremer, and Mullainathan find that nonlinear contract incentives can induce up-front

productivity

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Conclusion

• Reasonable justification provided that both government agents and contractor management portray time-inconsistent behavior o May lead to poor contract performance and cost growth

• Importance of institutional arrangements and human behavior in cost outcomeso e.g. commitment mechanisms to overcoming time-inconsistency

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Questions&

Answers

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BACK-UP

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Source: Office of Management and Budget (OMB), USASpending.gov.

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Source: Yahoo! Finance datasets. Defense Stock Index includes equal weights Lockheed Martin, General Dynamics, Boeing, Northrop Grumman, and Raytheon. Spread calculated as Defense Index (1.0 = Dec. 31, 1981) minus the S&P 500 Index (1.0 = Dec. 31, 1981). Accessed Nov. 22, 2014.